On Friday, Mrs May warned “no-one will get everything they want” from talks.

EU officials are now scrutinising Mrs May’s speech ahead of a fresh round of negotiations next week.

Speaking at London’s Mansion House, the prime minister set out the UK’s hopes for a future EU economic partnership, calling for “pragmatic common sense” in negotiations.

Single market access would be “less than it is now”, she said, and the UK would have to pay into some EU agencies.

But the prime minister said she would not threaten to walk out of talks and in a message to the EU added: “Let’s get on with it.”

She said all sides of the argument had to now face “hard facts”.

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Media captionTheresa May’s full Brexit speech where she said: “We chose to leave, we have a responsibility to help find a solution”

In his reaction, Mr Rees-Mogg praised her “good speech”, saying it delivered on the government’s promise to take the UK out of the customs union, the single market and the European Court of Justice.

“There are inevitably a few small points that will concern Leave campaigners but we must all recognise that everyone will have to give up something to get a deal, so now is not the time to nitpick,” he wrote.

He accused the EU of risking a “no deal” Brexit with its “absurd” suggestion that Northern Ireland should be in a common regulatory area with Brussels to avoid a hard border.

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In her speech, Mrs May said she was confident remaining differences over a draft EU legal agreement could be resolved, allowing trade talks to get under way.

She said life would be different for the UK outside the EU’s single market: “In certain ways, our access to each other’s markets will be less than it is now.”

The UK could not expect to “enjoy all the benefits without all of the obligations” of membership.

Another “hard fact” would be that the UK would still continue to be affected by EU law and some decisions of the European Court of Justice – such as the ECJ rules on whether EU agreements are legal.

However, she stressed the “jurisdiction of the European Court of Justice in the UK must end”.

The UK may choose to remain “in step” with EU regulations in areas like state aid and competition, in order to get “good access” to markets, she said.

The hard fact for the EU was that the UK would want its own bespoke trade deal, not an “off-the-shelf model”.

BBC political correspondent Alex Forsyth said “the real test will be whether this speech was enough to convince critics that Mrs May’s ambition for Brexit is credible and achievable without alienating her own MPs”.